Active Exploration for Robust Object Detection
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Citation
Javier Velez, Garrett Hemann, Albert S. Huang, Ingmar Posner, and
Nicholas Roy "Active Exploration for Robust Object Detection." Int.
Joint Conf. on Artificial Intelligence (IJCAI), Barcelona, Spain, Jul.
2011
As Published
http://ijcai-11.iiia.csic.es/program/paper/37
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Author's final manuscript
Citable link
http://hdl.handle.net/1721.1/67293
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
Active Exploration for Robust Object Detection
Javier Velez
†Garrett Hemann
†Albert S. Huang
†Ingmar Posner
‡Nicholas Roy
††MIT Computer Science and ‡Mobile Robotics Group
Artificial Intelligence Laboratory Dept. of Engineering Science, Oxford University
Cambridge, MA, USA Oxford, UK
Abstract
Today, mobile robots are increasingly expected to operate in ever more complex and dynamic envi-ronments. In order to carry out many of the higher-level tasks envisioned a semantic understanding of a workspace is pivotal. Here our field has benefited significantly from successes in machine learning and vision: applications in robotics of off-the-shelf object detectors are plentiful. This paper outlines an online, any-time planning framework enabling the active exploration of such detections. Our ap-proach exploits the ability to move to different van-tage points and implicitly weighs the benefits of gaining more certainty about the existence of an object against the physical cost of the exploration required. The result is a robot which plans trajecto-ries specifically to decrease the entropy of putative detections. Our system is demonstrated to signif-icantly improve detection performance and trajec-tory length in simulated and real robot experiments.
INTRODUCTION
Years of steady progress in robotic mapping and navigation techniques have made it possible for robots to construct accu-rate traversability maps of relatively complex environments and to robustly navigate within them (see, for example New-man et al., 2009). Such maps generally represent the world as regions which are traversable by a robot and regions which are not (see Fig. 1(a)) and are ideal for low-level navigation tasks such as moving through the environment without col-lisions. However, mobile robots are increasingly tasked to perform high-level requests in complex and dynamic envi-ronments. Sophisticated interactions between an agent and its workspace require the addition of semantic information into traditional environment representations, such as information about the location and identity of objects in the workspace (see Fig. 1). For example, a cleaning robot knows that dirty dishes are usually on top of tables and benefits from knowing where the tables are in the environment.
This work was performed under NSF IIS Grant #0546467 and ONR MURI N1141207-236214 and their support is gratefully ac-knowledged.
Recently, advances in vision- and laser-based object recog-nition have been leveraged to enrich maps with higher-order, semantic information (e.g., Posner, Cummins, and Newman, 2009; Douillard, Fox, and Ramos, 2008; Mozos, Stachniss, and Burgard, 2005; Anguelov et al., 2004). A straightfor-ward approach to adding semantic information is to accept the results of a standard object detector framework prima fa-cie, irrespective of sensor noise. A consequence of directly using the results of an object detector is that the quality of the map built strongly depends on the shortcomings of the object detector. Vision-based object detection, for example, is often-times plagued by significant performance degradation caused by a variety of factors including a change of aspect compared to that encountered in the training data and, of course, oc-clusion (e.g., Coates and Ng, 2010; Mittal and Davis, 2008). Both of these factors can be addressed by choosing the loca-tion of the camera carefully before acquiring an image and performing object detection.
Rarely, however, are the capabilities of the mobile robot building the map exploited to improve the robustness of the detection process by specifically counteracting known detec-tor issues. Rather than placing the burden of providing per-fect detections with the detector itself, the robot can act to improve its perception.
In this work, we explore how a robot’s ability to selectively gather additional information about a possible object by mov-ing to a specified location — a key advantage over more con-ventional, static deployment scenarios for object detectors — can improve the precision of object detections included in the map. In particular, we propose a planning framework that reasons about taking detours from the shortest path to a goal in order to explore potential object detections based on noisy observations from an off-the-shelf object detector. At each step, the agent weighs the potential benefit of increasing its confidence about a potential object against the cost of taking a detour to a more suitable vantage point.
We make two primary contributions in this paper. Firstly, we explicitly incorporate the costs of motion when planning sensing detours. Secondly, we give an approximate sensor model that captures correlations between subsequent obser-vations. objects). Previous work has largely ignored motion costs and has typically assumed observations are condition-ally independent given the sensor position. Inspired by recent progress in forward search for planning under uncertainty, we
(a) (b)
Figure 1: A traditional environment map (a) with regions that are traversable (cyan) and not (red) useful for navigation, (b) the traversable map augmented with semantic information about the identity and location of objects in the world allow-ing for richer interactions between agent and workspace.
show that motion costs can be incorporated and measurement correlations modeled, allowing us to efficiently find robust observation plans.1
RELATED WORK
Planning trajectories for a mobile sensor has been explored in various domains. The approach presented here is inspired by forward search strategies for solving partially observable Markov decision processes (Ross et at., 2008; Prentice and Roy, 2009) but incorporates a more complex model that ap-proximates the correlations between observations.
The controls community and sensor placement commu-nity formulate the problem as minimizing a norm of the posterior belief, such as entropy, without regard to motion cost. As a consequence, greedy strategies that choose the next-most valuable measurement can be shown to be bound-edly close to the optimal, and the challenge is to generate a model that predicts this next-best measurement (Guestrin, Krause, and Singh, 2005; Krause et al., 2008). Formulat-ing the information-theoretic problem as a decision-theoretic POMDP Sridharan, Wyatt, and Dearden (2008) showed that true multi-step policies did improve the performance of a computer vision system in terms of processing time. How-ever, the costs of the actions are independent (or negligible), leading to a submodular objective function and limited im-provement over greedy strategies.
A few relevant pieces of work from the active vision do-main include Arbel and Ferrie (1999) and more recently La-porte and Arbel (2006) who use a Bayesian approach to model detections that is related to ours, but only search for the next-best viewpoint, rather than computing a full plan. The work of Deinzer, Denzler, and Niemann (2003) is per-haps most similar to ours in that the viewpoint selection prob-lem is framed using reinforcement learning, but again the au-thors “neglect costs for camera movement” and identify the absence of costs as a limitation of their work.
The contribution of our work over the existing work is pri-marily to describe a planning model that incorporates both action costs and detection errors, and specifically to give an approximate observation model that captures the correlations
1
This paper presents results that originally appeared at ICAPS 2011 (Velez et al., 2011).
(a) (b)
Figure 2: A conceptual illustration of (a) the robot at view-point x while following the original trajectory (bold line) to-wards the goal (red star), (b) the perception field for a par-ticular object detector centered around an object hypothesis and alternative path (bold dash-dotted line) taken by a curious robot to investigate the object of interest. Lighter cell shad-ing values indicate a lower conditional entropy and therefore desirable vantage points.
between successive measurements that still allows forward-search planning to operate, leading to an efficient multi-step search to improve object detection.
PROBLEM FORMULATION
Consider an agent navigating through an environment with potential objects of interest at unknown locations. The agent has a goal destination but is allowed to inspect the locations of said objects of interest; for example, a rescue robot look-ing for people in a first-responder scenario. Traditionally, an object detector is used at waypoints along the way and an ob-ject is either accepted into the map or reob-jected based upon a simple detector threshold.
However, the lack of introspection of this approach regard-ing both the confidence of the object detector and the quality of the data gathered can lead to an unnecessary acceptance of spurious detections; what looked like a ramp from a particu-lar viewpoint may in fact have been a trick of the light. Most systems simply discard lower confidence detections, and have no way to improve the estimate with further, targeted mea-surements. In contrast, we would like the robot to modify its motion to both minimize total travel cost and the cost of errors when deciding whether or not to add newly observed objects to the map.
Let us represent the robot as a point x ∈ R2; without loss
of generality, we can express a robot trajectory as a set of waypoints x1:K. As the robot moves, it receives output from its object detector that gives rise to a belief over whether a detected object truly exists at the location indicated. Let the presence of an object at some location (x, y) be captured by the random variable Y ∈ {object, no-object}2. Let us also de-fine a decision action a ∈ {accept, reject}, where the detected object is either accepted into the map (the detection is deter-mined to correspond to a real object) or rejected (the detection is determined to be spurious). Additionally, we have an
ex-2We assume the robot knows its own location, and has a
suffi-ciently well-calibrated camera to assign the location of the object. In this work, the uncertainty is whether or not an object is present at the given location (x, y).
plicit cost ξdec : {accept, reject} × {object, no-object} 7→ R
for a correct or incorrect accept or reject decision. We cannot know the true costs of the decisions because we ultimately do not know the true state of objects in the environment. But, we can use a probabilistic sensor model for object detections to minimize the expected cost of individual decision actions ξdec
given the prior over objects. We therefore formulate the plan-ning problem as choosing a sequence of waypoints to mini-mize the total travel cost along the trajectory and the expected costs of the decision actions at the end of the trajectory.
OBJECT DETECTION SENSOR MODEL
In order to compute the expected cost of decision actions, we must estimate the probability of objects existing in the world, and therefore require a probabilistic model of the object de-tector. The key idea is that we model the object detector as a spatially varying process; around each potential object, we characterize every location with respect to how likely it is to give rise to useful information.
A measurement, z, at a particular viewpoint consists of the output of the object detector, assumed to be a real number indicating the confidence of the detector that an object exists. The distribution over the range of confidence measurements is captured by the random variable Z defined over a range Z of discretized states (bins). At every location x the posterior distribution over Y can be expressed as
p(y|z, x) = Pp(z|y, x)p(y)
y0p(z|y0, x)p(y0)
, (1)
where p(z|y, x) denotes the likelihood of observing a partic-ular detector confidence at x given the true state of the object. This likelihood can be obtained empirically.
When observations originate from a physical device such as a camera, a straightforward approach is to treat observa-tions as conditionally independent given the state of the robot (see Fig. 3(a)). This model is easy to work with, but assumes that measurements vary only as a result of sensor noise and the object state. In practice, measurements vary as a function of many different factors such as scene geometry, lighting, oc-clusion, etc. The approach in Fig. 3(a) simply ignores these factors. If all of these (often unobservable) sources of varia-tion were correctly modeled and estimated in a environmen-tal variable Ψ (Fig. 3(b)), then the conditional independence would hold, but constructing and maintaining a model suffi-cient to capture the image generation process is an intractable computational and modeling burden.
To correct our observation model without an explicit model Ψ, we can maintain a history of observation view-points. As more viewpoints are visited, knowledge regard-ing Y and future observations can be integrated recursively. As shown in Fig. 3(c), we remove Ψ and add a depen-dency between previous viewpoints and the current obser-vation zK. Let TK denote a trajectory of K locations
tra-versed in sequence. At each location a measurement is obtained, giving a possible detection and the correspond-ing confidence. The trajectory is thus described by a set TK = {{x1, z1}, {x2, z2}, . . . , {xK, zK}} of K
location-observation pairs. Knowledge gained at each step along the
trajectory can be integrated into the posterior distribution over Y such that
p(y|TK) = p(z
K|y, xK, TK−1)p(y|TK−1)
p(zK|xK, TK−1) , (2)
where zKis the Kthobservation, which depends not only on the current viewpoint but also on the history of measurements TK−1. In principle, K can be arbitrarily long, so the primary
challenge is to develop an efficient way of conditioning our observation model on previous viewpoints.
To overcome this difficulty, we approximate the real pro-cess of object detection with a simplistic model of how the images are correlated. We replace the correlating influence of environment Ψ with a convex combination of a fully uncorre-lated and a fully correuncorre-lated model such that the new posterior belief over the state of the world is computed as
p(y|TK) = (1−α)p(z K|y, xK) p(zK|xK) + α p(y|TK−1) (3) This captures the intuition that repeated observations from the same viewpoint add little to the robot’s knowledge about the state of the world. Observations from further afield, however, become increasingly independent; Ψ has less of a correlating effect. The mixing parameter, α, can be chosen such that no information is gained by taking additional measurements at the same location and the information content of observations increases linearly with distance from previous ones (see Velez et al., 2011).
Perception Field
Using the observation model and Equ. 3, it is possible to eval-uate how much additional information a future viewpoint xK
provides on the object state Y . Given xK and the trajectory TK−1 visited thus far, the expected reduction in uncertainty
is captured by the mutual information between Y and the ob-servation Z received at xK:
I(Y, Z; xK, TK−1) = (4) H(Y ; TK−1) − H(Y |Z; xK, TK−1), Of these two terms, the first H(Y ; TK−1) term is
indepen-dent of xK and can be ignored. The second term, the
con-ditional entropy, can be readily evaluated using empirically determined quantities. In particular, we use the conditional entropy evaluated at all viewpoints in the robot’s surrounding workspace to form the perception field (Velez et al., 2011) for a particular object hypothesis (see Fig. 2(b)). This field de-notes locations with high expected information gain. Due to the correlations between individual observations made over a trajectory of viewpoints, the perception field changes as new observations are added. Note that if the robot’s only goal was to determine Y with the greatest confidence, it would repeatedly visit locations with least conditional entropy, as indicated by the perception field.
PLANNING DETOURS
We now describe a planning algorithm that trades off the ben-efit of gaining additional information about an object hypoth-esis against the operational cost of obtaining this information.
(a) (b) (c)
Figure 3: Different graphical models representing the observation function. (a) A naive Bayes approximation, that assumes that every observation is conditionally independent given knowledge of the object. (b) The true model that assumes that observations are independent given knowledge of the environment and the object. (c) The model employed here, in which the correlations are approximated by way of a mixture model parameterized by α as per Equ. 3.
When an object is first detected, a new path to the orig-inal goal is planned based on the total cost function, which includes both the motion cost along the path and the value of measurements from locations along the path, expressed as a reduction in the expected cost of decision actions. The cost function consists of two terms: the motion cost cmot(x1:K)
and the decision cost cdec(x1:K, a), such that the optimal plan
π∗is given by π∗= arg min
x1:K,a
cmot(x1:K) + cdec(x1:K, a) , (5)
cdec(x1:K, a) = Ey|x1:K[ξdec(a, y)], (6)
where Ey|x1:K[·] denotes the expectation with respect to the
robot’s knowledge regarding the object, after having executed path x1:K. We choose c
mot(x1:K) to be a standard motion
cost function proportional to the path length.
The planning process therefore proceeds by searching over sequences of x1:K, evaluating paths by computing expecta-tions with respect to both the observation sequences and the object state. The paths with the lowest decision cost will tend to be those leading to the lowest posterior entropy, avoiding the large penalty for false positives or negatives.
Multi-step Planning A naive approach to searching over trajectories scales exponentially with the planning horizon K and rapidly becomes intractable as more observations are considered. We therefore adopt a roadmap scheme in which a fixed number of locations are sampled every time a new viewpoint is to be added to the current trajectory. A graph is built between the sampled poses, with straight-line edges be-tween samples. The perception field is used to bias sampling towards locations with high expected information gain.
The planning approach described so far can be extended to planning in an environment with M object hypotheses by considering a modified cost function which simply adds the cost for each object and treating the existence of each object independently such that individual perception fields add at a particular location. See Velez et al. (2011) for more details.
EXPERIMENTS
We tested our approach on both a simulated robot with an em-pirically derived model of an object detector and on an actual
Figure 4: Robotic wheelchair platform
autonomous wheelchair (Fig. 4) using a vision-based object detector (Felzenszwalb, McAllester, and Ramanan, 2008). In both the simulation and physical experiments, the robot was tasked with reaching a manually specified destination. The robot was rewarded for correctly detecting and reporting the location of doors in the environment, penalized for false alarms, and incurred a cost proportional to the length of its total trajectory. We chose doors as objects of interest due to their abundance in indoor environments and their utility to mobile robots – identifying doorways is often a component of higher level tasks.
Our autonomous wheelchair is equipped with onboard laser range scanners, primarily used for obstacle sensing and navigation, and a Point Grey Bumblebee2 color stereo cam-era. The simulation environment is based on empirically con-structed models of the physical robot and object detector. We set ξdec(reject, ·) to zero, indicating no penalty for missed
ob-jects.
Learned Perception Field
Fig. 5 shows the perception field for the detector model learned from 3400 training samples, with each cell indicat-ing the conditional entropy of the posterior distribution over
Average Randomβ=0.8 Randomβ=0.6 Greedyβ=0.8 Greedyβ=0.6 Planned RTBSS
Precision 0.27 ±0.03 0.26 ±0.04 0.31 ±0.06 0.60 ±0.07 0.75 ±0.06 0.45 ±0.06 Recall 0.72 ±0.06 0.60 ±0.07 0.44 ±0.07 0.62 ±0.07 0.80 ±0.06 0.58 ±0.07 Path Length (m) 62.63 ±0.02 62.03 ±0.67 67.08 ±2.23 41.95 ±0.88 54.98 ±3.04 47.57 ±0.19
Total Trials 50 50 50 50 50 50
Table 1: Simulation performance on single door scenario, with standard error values.
Average Randomβ=0.8 Randomβ=0.6 Greedyβ=0.8 Greedyβ=0.6 Planned RTBSS
Precision 0.64 ±0.03 0.67 ±0.03 0.64 ±0.03 0.54 ±0.03 0.53 ±0.05 0.70 ±0.03 Recall 0.64 ±0.04 0.69 ±0.03 0.63 ±0.02 0.57 ±0.03 0.76 ±0.03 0.66 ±0.03 Path Length (m) 199.62 ±11.24 161.36 ±6.13 153.32 ±4.37 121.35 ±1.32 138.21 ±7.12 160.74 ±6.08
Total Trials 50 50 50 50 50 50
Table 2: Simulation performance on multiple door scenario, with standard error values.
Figure 5: Learned perception field for a possible door. The unknown object is centered at the origin (blue). Brighter re-gions correspond to viewpoints more likely to result in higher confidence posterior beliefs.
the true state of an object given an observation from this view-point, p(y|z, x) and a uniform initial belief. Intuitively, this suggests that the viewpoint from which a single observation is most likely to result in a low-entropy posterior belief is ap-proximately 9 m directly in front of the door. Viewpoints too close to or far from the door, and those from oblique angles are less likely to result in high-confidence posterior beliefs.
Simulation Results
We first assessed our planning approach using the learned model in a simulated environment. Our simulation environ-ment consisted of a robot navigating through an occupancy map, with object detections triggered according to the learned object detection model and correlation model α. We also simulated false positives by placing non-door objects that probabilistically triggered object detections using the learned model for false-alarms. The processing delay incurred by the actual object detector was also simulated (the object detector requires approximately 2 seconds to process a spatially deci-mated 512x384 pixel image).
Comparison Algorithms
For the simulation trials we compared our algorithm against three other algorithms. The Randomβ algorithm repeatedly
obtained observations from randomly selected viewpoints near detected objects until the belief of each object exceeded a threshold β, and then continued on to the original destina-tion. The Greedyβalgorithm selected the best viewpoint
ac-cording to our perception field for each potential object until
Figure 6: Simulation scenario with multiple doors (cyan triangles) and non-doors (black bars). The robot starts at the bottom-left (S) with a goal near the bottom-right (G). The robot’s object detector responds to both doors and non-doors. Top: example trajectory (purple) executed using ran-dom viewpoint selection. Bottom: example trajectory (pur-ple) executed using planned viewpoints.
the belief of each object exceeded a threshold β. Lastly, we compared our algorithm against the RTBSS online POMDP algorithm (Paquet, Tobin, 2005) with a maximum depth of 2. Single Door Simulation
First, we tested our planning algorithm on a small simulation environment with one true door and two non-doors. Table 1 shows the results of 50 trials. Overall, explicitly planning viewpoints resulted in significantly higher performance. The planned viewpoints algorithm performed better than RTBSS in terms of precision and recall, most likely because our algo-rithm sampled continuous-space viewpoints and the RTBSS algorithm had a fixed discrete representation, while RTBSS paths were shorter.
Multi Door Simulation
Next, we evaluated our algorithm in a larger, more complex scenario containing four doors and six non-door objects. Fig-ure 6 shows the multiple door simulation environment and
ex-Figure 7: Trajectory executed on the actual robot wheelchair using planned viewpoints from ’S’ to ’G’ where the robot dis-covers one true door (cyan triangle). Near the goal, it detects two more possible doors (red dots), detours to inspect them, and (correctly) decides that they are not doors.
Average Greedyβ=0.8 Planned
Precision 0.53 ±0.14 0.7 ±0.15 Recall 0.60 ±0.14 0.7 ±0.15 Path Length (m) 153.86 ±33.34 91.68 ±15.56 Total Trials 10 10
Table 3: Results of real-world trials using robot wheelchair.
ample trajectories planned and executed by the planned and Randomβalgorithms.
Table 2 shows the simulation results for the multi-door sce-nario. Our planned viewpoints algorithm resulted in the sec-ond shortest paths after Greedyβ=0.6but with superior
detec-tion performance. Planned viewpoints also resulted in signif-icantly shorter paths than RTBSS given the same operating point on the ROC curve.
Physical Wheelchair Trials
We conducted a small experiment comparing our planned viewpoints algorithm and the Greedyβ=0.8 on a robot
wheelchair platform. The robot was given a goal position such that a nominal trajectory would bring it past one true door, and near several windows that trigger object detections. Figure 7 illustrates the trajectory executed during a single trial of the planned viewpoints algorithm, and Table 3 sum-marizes the results of all trials. Our planned viewpoints algo-rithm resulted in significantly shorter trajectories while main-taining comparable precision and recall. For doors detected with substantial uncertainty, our algorithm planned more ad-vantageous viewpoints to increase its confidence and ignored far away detections because of high motion cost.
CONCLUSIONS AND FUTURE WORK
Previous work in planned sensing has largely ignored motion costs of planned trajectories and used simplified sensor mod-els with strong independence assumptions. In this paper, we presented a sensor model that approximates the correlation in observations made from similar vantage points, and an effi-cient planning algorithm that balances moving to highly in-formative vantage points with the motion cost of taking
de-tours. The result is a robot which plans trajectories specifi-cally to decrease the entropy of putative detections. The per-formance of our algorithm could be further improved by fu-ture work in both the sensor model and planning technique.
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